TNT Motorsports Park in Chester S.C. has a dedicated track for small bikes. Just west off I-77, south of Charlotte. Also has 4 other tracks with one that 50's could navigate easily but may have big bikes on it from time to time, has some fun trails etc. Open basically everyday unless the weather is a problem.
I was a member there for a few years when I lived in SC. Some people bag on the place and lady owner but I always had a good time there and enjoyed the variety.
I just noticed AMA members get 15% off the best available rate at Comfort Inns.
Discount code #00947556
Seems to me the rooms were $85, makes then $68.
Nice discount!